How to Simplify the Expression m/(m-6) + m/7 for 11-Year-Old Students

Learn step-by-step how to simplify the expression m divided by (m minus 6) plus m divided by 7, perfect for 11-year-old students.

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Let's simplify the expression m/(m-6) + m/7 step by step.

  1. Understand the problem: We want to add two fractions: m/(m-6) and m/7. Since they have different denominators, we need to find a common denominator.
  2. Find the common denominator: The denominators are m-6 and 7. The common denominator will be the product of both: 7(m-6).
  3. Rewrite each fraction with the common denominator:
    • First fraction: m/(m-6) can be written as (m * 7) / [7(m-6)] to have denominator 7(m-6).
    • Second fraction: m/7 can be written as [m * (m-6)] / [7(m-6)].
  4. Add the numerators: Now we add the two fractions:

    (7m + m(m - 6)) / [7(m-6)]
  5. Simplify the numerator: Expand m(m - 6):
    m * m = m2
    m * (-6) = -6m
    So, m(m - 6) = m2 - 6m.

    Now the numerator becomes:
    7m + m2 - 6m = m2 + (7m - 6m) = m2 + m.
  6. Final expression:
    (m2 + m) / [7(m-6)]
  7. Optional factorization:
    You can factor the numerator:
    m2 + m = m(m + 1)
    So the simplified expression is:
    m(m + 1) / [7(m - 6)].

Final answer:
m(m + 1) / [7(m - 6)]

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